The entries in a certain row of Pascal's triangle are \[1, n, \dots, n, 1.\] The average of the entries in this row is 2. Find $n$.
The average will be 2^n / (n + 1) where n is the row number = 0,1,2,3........
So
2^(n ) / (n + 1) = 2
2^(n) = 2(n + 1)
From inspection, we can determine that n = 3
1
1 1
1 2 1
1 3 3 1 → 3td row
+585 
